JHU-UMD Complex Geometry Seminar Archives for Fall 2024 to Spring 2025
Mean curvature flow in spaces with positive cosmological constant
When: Tue, September 19, 2023 - 3:30pmWhere: Kirwan Hall 1313
Speaker: Or Hershkovits (Hebrew University of Jerusalem) -
Abstract: In this talk, I will describe an approach of using Lorentzian mean curvature flow (MCF) to probe cosmologies satisfying the Einstein equation with positive cosmological constant with matter obeying the strong energy conditions. Assuming surface symmetry, I will explain how such flow converges, in some sense, to the standard constant mean curvature (CMC) slicing of de Sitter space. I will then illustrate a condition, natural in the above context, such that any local graphical mean curvature flow (without symmetry) in de Sitter space satisfying that condition converges to the standard CMC slicing of the entire de Sitter space. This is based on joint works with Creminelli, Senatore and Vasy, and on a joint work with Senatore.
The inverse spectral problem for ellipses
When: Wed, March 13, 2024 - 4:30pmWhere: JHU, Maryland Building, room 114
Speaker: Hamid Hezari (UC Irvine) -
Abstract: This talk is about Kac‘s inverse problem from 1966: "Can one hear the shape of a drum?" The question asks whether the frequencies of vibration of a bounded domain determine the shape of the domain. First we present a quick survey on the known results. Then we discuss the key connection between eigenvalues of the Laplacian and the dynamics of the billiard, which is governed by the so called “Poisson Summation Formula“. Finally we discuss our main theorem that "one can hear the shape of nearly circular ellipses". This was a joint work with Steve Zelditch (9/13/1953 – 9/11/2022).
TBA
When: Mon, April 15, 2024 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Ravi Vakil (Stanford) -
Abstract: TBA
K-stability of log Fano pairs of Maeda type
When: Fri, May 17, 2024 - 4:00pmWhere: MATH 1310
Speaker: Konstantin Loginov (Moscow) -
Abstract: We will discuss K-stability of Fano varieties of lower dimensions, and also of log Fano pairs of some special type. K-stability is an algebraic invariant that characterises the existence of a Kahler-Einstein metrics on Fano varieties. Initially, this invariant was defined in terms of all one-parameter degenerations of a given variety. Later, Fujita and Li proposed a valuative criterion of K-stability which allows to check it in terms of numerical invariants of divisors over given variety. Using this criterion and the inductive approach by Abban-Zhuang, a group of 9 authors solved the problem of characterisation of K-stable varieties for a general element in each of 105 families of smooth Fano threefolds. I will consider an analogous problem for three-dimensional log Fano varieties, that is, pairs (X, D) with boundary divisor D, such that - K_X - D is ample. I will concentrate on so-called log Fano pairs of Maeda type, introduced by Fujita. To solve this problem, we will develop a generalisation of Abban-Zhuang theory, as well as the classification of log smooth log Fano pairs in dimension 3 due to Maeda.